Terry Snow wanted to know how to tell if two arbitrary precision numbers
are the same even including the bits that are not known reliably. Consider
the following:
In[1]:= $Pre=InputForm;
In[2]:= x1=N[1/10,18]
Out[2]= 0.100000000000000000000000000005049`18
In[3]:= x2=x1+10^-32
Out[3]= 0.100000000000000000000000000005059`18
Others suggested using RealDigits, but it seems RealDigits doesn't tell us
about digits that may be wrong.
In[4]:= RealDigits[x1]
Out[4]= {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, 0}
Instead do the following. The result is zero if and only if the numbers
are the same.
In[5]:= SetPrecision[x2-x1,Infinity]
Out[5]= 1/81129638414606681695789005144064
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Ted Ersek